Lesson 5

More Dilations

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Problem 1

Quadrilateral \(ABCD\) is dilated with center \((0,0)\), taking \(B\) to \(B'\). Draw \(A'B'C'D'\).

A quadrilateral, A, negative 2 comma 3, B, 3 comma 1, C, 1 comma negative 1, D, negative 3 comma negative 2. Another point, B prime, 6 comma 2.

Solution

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Problem 2

Triangles \(B\) and \(C\) have been built by dilating Triangle \(A\).

Three triangles, 2 of which are dilations of the first.  Please ask for further assistance.
  1. Find the center of dilation.
  2. Triangle \(B\) is a dilation of \(A\) with approximately what scale factor?
  3. Triangle \(A\) is a dilation of \(B\) with approximately what scale factor?
  4. Triangle \(B\) is a dilation of \(C\) with approximately what scale factor?

Solution

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Problem 3

Here is a triangle.

  1. Draw the dilation of triangle \(ABC\), with center \((0,0)\), and scale factor 2. Label this triangle \(A’B’C’\).
  2. Draw the dilation of triangle \(ABC\), with center \((0,0)\), and scale factor \(\frac{1}{2}\). Label this triangle \(A’’B’’C’’\).
  3. Is \(A’’B’’C’’\) a dilation of triangle \(A’B’C’\)? If yes, what are the center of dilation and the scale factor?
Coordinate plane, x, negative 7 to 8, y, negative 6 to 6. A triangle, A, 4 comma negative 2, B, negative 2 comma negative 2, C, negative 2 comma 2.

 

Solution

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Problem 4

Triangle \(DEF\) is a right triangle, and the measure of angle \(D\) is \(28^\circ\). What are the measures of the other two angles? 

Solution

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(From Unit 1, Lesson 15.)